A shoot-out raged in this Dorchester neighborhood Sunday night, and when it ceased a young man staggered to the front door of 93 Brook Ave., where he pushed on the intercom and collapsed, witnesses said.

The victim, shot in the chest, was gasping for air as an unidentified woman opened the door. The wounded man uttered, “I can’t breathe,’’ witnesses said. The woman told him to stay awake and just try to keep breathing.